factor expression

Question

Factor the expression. y2 + 10xy + 25x2

(y - 5x)²

(y + 5x)²

(y + 5x)(y - 5x)

Prime Polynomial

Answer 1

We want to factor y² + 10xy + 25x².

 

One way to do so is to look at the product of the coefficients of y² and x² and check to see if any factor pairs sum to the coefficient of xy.

 

Here (1)(25) = 25 and its factor pairs are 1 & 25, and 5 & 5.  5 + 5 = 10, so we can rewrite the xy term as 10xy = 5xy + 5xy.

 

 

y² + 10xy + 25x² = y² + (5xy + 5xy) + 25x²

 

 

= (y² + 5xy) + (5xy + 25x²) = y(y + 5x) + 5x(y + 5x)

 

 

= (y + 5x)(y + 5x) = (y + 5x)²